Subgroups — C₂×C₆₇×#3547 #30742001

Order 17152.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3547	C₂	1	32	yes	maximal, direct product factor
2	C₂×#562×C₆₇	C₂	1	4	yes	maximal, complemented
3	C₂×#555×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×#555×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#554×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#553×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#552×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×D₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#548×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#544×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₂×#542×C₆₇	C₂	1	4	yes	maximal, complemented
13	C₂×#540×C₆₇	C₂	1	2	yes	maximal, complemented
14	C₂×#537×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₂×#536×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41×C₆₇	C₂²	1	2	yes	—
20	C₂²×#41×C₆₇	C₂²	1	2	yes	—
21	C₂³×Q₈×C₆₇	C₂²	1	2	yes	—
22	#562×C₆₇	C₂²	1	64	yes	complemented
23	#555×C₆₇	C₂²	1	32	yes	complemented
24	#555×C₆₇	C₂²	1	16	yes	complemented
25	#554×C₆₇	C₂²	1	16	yes	complemented
26	#553×C₆₇	C₂²	1	32	yes	complemented
27	#552×C₆₇	C₂²	1	32	yes	complemented
28	D₄×Q₈×C₆₇	C₂²	1	16	yes	complemented
29	#548×C₆₇	C₂²	1	32	yes	complemented
30	#547×C₆₇	C₂²	1	16	yes	complemented
31	#544×C₆₇	C₂²	1	32	yes	complemented
32	#542×C₆₇	C₂²	1	64	yes	complemented
33	#540×C₆₇	C₂²	1	32	yes	complemented
34	#537×C₆₇	C₂²	1	32	yes	complemented
35	#536×C₆₇	C₂²	1	32	yes	complemented
36	#533×C₆₇	C₂²	1	16	yes	complemented
37	#532×C₆₇	C₂²	1	16	yes	complemented
38	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₆₇	C₂²	1	4	yes	—
42	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
43	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
44	#529×C₆₇	C₂²	1	16	yes	complemented
45	C₂×#126×C₆₇	C₂²	1	2	yes	—
46	C₂×#126×C₆₇	C₂²	1	4	yes	—
47	C₂×#125×C₆₇	C₂²	1	4	yes	—
48	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
49	C₂×#125×C₆₇	C₂²	1	2	yes	—
50	C₂×#125×C₆₇	C₂²	1	2	yes	—
51	C₂×#124×C₆₇	C₂²	1	4	yes	—
52	C₂×#124×C₆₇	C₂²	1	4	yes	—
53	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×#124×C₆₇	C₂²	1	2	yes	—
55	C₂×#124×C₆₇	C₂²	1	4	yes	—
56	C₂×#123×C₆₇	C₂²	1	2	yes	—
57	C₂×#123×C₆₇	C₂²	1	4	yes	—
58	C₂×#123×C₆₇	C₂²	1	4	yes	—
59	C₂×#123×C₆₇	C₂²	1	4	yes	—
60	C₂×#123×C₆₇	C₂²	1	4	yes	—
61	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
62	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
63	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
64	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
65	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
67	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
68	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
69	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
70	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
71	C₂×#121×C₆₇	C₂²	1	2	yes	—
72	C₂×#121×C₆₇	C₂²	1	4	yes	—
73	C₂×#121×C₆₇	C₂²	1	4	yes	—
74	C₂×#121×C₆₇	C₂²	1	4	yes	—
75	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
76	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
77	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
78	C₂×#121×C₆₇	C₂²	1	4	yes	—
79	C₂×#121×C₆₇	C₂²	1	2	yes	—
80	C₂×#121×C₆₇	C₂²	1	2	yes	—
81	C₂×#121×C₆₇	C₂²	1	2	yes	—
82	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
83	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
84	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
85	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
86	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
87	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
88	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
89	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
90	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
91	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
92	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
93	C₂×#117×C₆₇	C₂²	1	2	yes	—
94	C₂×#117×C₆₇	C₂²	1	2	yes	—
95	C₂×#117×C₆₇	C₂²	1	2	yes	—
96	C₂×#117×C₆₇	C₂²	1	4	yes	—
97	C₂×#117×C₆₇	C₂²	1	2	yes	—
98	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
101	C₂×#41×C₆₇	—	4	8	no	—
102	C₂×#41×C₆₇	—	4	8	no	—
103	C₂×#41×C₆₇	C₂³	1	16	yes	—
104	C₂×#41×C₆₇	C₂³	1	16	yes	—
105	C₂²×Q₈×C₆₇	—	4	8	no	—
106	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
108	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
110	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
111	C₂²×Q₈×C₆₇	C₂³	1	16	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
116	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
119	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
120	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
121	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
125	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
126	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
129	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
130	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
131	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
132	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
133	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
134	C₄⋊Q₈×C₆₇	C₂³	1	32	yes	—
135	C₄⋊Q₈×C₆₇	C₂³	1	16	yes	—
136	#127×C₆₇	C₂³	1	8	yes	—
137	#126×C₆₇	C₂³	1	16	yes	—
138	#126×C₆₇	C₂³	1	32	yes	—
139	#125×C₆₇	C₂³	1	8	yes	—
140	#125×C₆₇	C₂³	1	16	yes	—
141	#125×C₆₇	C₂³	1	32	yes	—
142	#125×C₆₇	C₂³	1	16	yes	—
143	#124×C₆₇	C₂³	1	8	yes	—
144	#124×C₆₇	C₂³	1	16	yes	—
145	#124×C₆₇	C₂³	1	32	yes	—
146	#124×C₆₇	C₂³	1	32	yes	—
147	#124×C₆₇	C₂³	1	32	yes	—
148	#123×C₆₇	C₂³	1	16	yes	—
149	#123×C₆₇	C₂³	1	32	yes	—
150	#123×C₆₇	C₂³	1	32	yes	—
151	#123×C₆₇	C₂³	1	32	yes	—
152	#123×C₆₇	C₂³	1	32	yes	—
153	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
154	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
155	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
156	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
157	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
158	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
159	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
160	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
161	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
162	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
163	#121×C₆₇	C₂³	1	8	yes	—
164	#121×C₆₇	C₂³	1	8	yes	—
165	#121×C₆₇	C₂³	1	8	yes	—
166	#121×C₆₇	C₂³	1	16	yes	—
167	#121×C₆₇	C₂³	1	32	yes	—
168	#121×C₆₇	C₂³	1	16	yes	—
169	#121×C₆₇	C₂³	1	32	yes	—
170	#121×C₆₇	C₂³	1	32	yes	—
171	#121×C₆₇	C₂³	1	16	yes	—
172	#121×C₆₇	C₂³	1	32	yes	—
173	#121×C₆₇	C₂³	1	16	yes	—
174	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
175	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
176	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
177	C₄×D₄×C₆₇	C₂³	1	8	yes	—
178	C₄×D₄×C₆₇	C₂³	1	16	yes	—
179	C₄×D₄×C₆₇	C₂³	1	8	yes	—
180	C₄×D₄×C₆₇	C₂³	1	16	yes	—
181	C₄×D₄×C₆₇	C₂³	1	8	yes	—
182	C₄×D₄×C₆₇	C₂³	1	16	yes	—
183	C₄×D₄×C₆₇	C₂³	1	16	yes	—
184	C₄×D₄×C₆₇	C₂³	1	32	yes	—
185	#117×C₆₇	C₂³	1	16	yes	—
186	#117×C₆₇	C₂³	1	16	yes	—
187	#117×C₆₇	C₂³	1	16	yes	—
188	#117×C₆₇	C₂³	1	32	yes	—
189	#117×C₆₇	C₂³	1	16	yes	—
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	—
197	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	—
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
207	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
208	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
209	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
231	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
232	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
233	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
234	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
235	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
236	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
237	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
238	#41×C₆₇	—	4	32	no	—
239	#41×C₆₇	—	4	32	no	—
240	C₂×Q₈×C₆₇	—	2	4	no	—
241	C₂×Q₈×C₆₇	—	2	8	no	—
242	C₂×Q₈×C₆₇	—	4	8	no	—
243	C₂×Q₈×C₆₇	—	4	4	no	—
244	C₂×Q₈×C₆₇	—	4	4	no	—
245	C₂×Q₈×C₆₇	—	4	32	no	—
246	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
248	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
249	C₂×Q₈×C₆₇	C₂⁴	1	16	yes	—
250	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
251	C₂×D₄×C₆₇	—	2	4	no	—
252	C₂×D₄×C₆₇	—	2	4	no	—
253	C₂×D₄×C₆₇	—	2	4	no	—
254	C₂×D₄×C₆₇	—	4	4	no	—
255	C₂×D₄×C₆₇	—	4	4	no	—
256	C₂×D₄×C₆₇	—	4	8	no	—
257	C₂×D₄×C₆₇	—	4	4	no	—
258	C₂×D₄×C₆₇	—	4	4	no	—
259	C₂×D₄×C₆₇	—	4	4	no	—
260	C₂×D₄×C₆₇	—	4	8	no	—
261	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
262	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
263	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
264	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
265	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
266	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
267	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
268	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
269	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
270	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
271	C₂²×C₄×C₆₇	—	2	8	no	—
272	C₂²×C₄×C₆₇	—	2	8	no	—
273	C₂²×C₄×C₆₇	—	2	4	no	—
274	C₂²×C₄×C₆₇	—	2	4	no	—
275	C₂²×C₄×C₆₇	—	2	8	no	—
276	C₂²×C₄×C₆₇	—	4	8	no	—
277	C₂²×C₄×C₆₇	—	4	2	no	—
278	C₂²×C₄×C₆₇	—	4	8	no	—
279	C₂²×C₄×C₆₇	—	4	8	no	—
280	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
282	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
283	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
284	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
285	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
295	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
297	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
298	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
300	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
303	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
305	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
306	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
307	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
308	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
309	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
310	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
311	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
312	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
313	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
314	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
315	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
316	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
317	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
318	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
319	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
320	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
321	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
322	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
323	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
324	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
325	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
326	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
327	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
328	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
329	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
330	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
331	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
332	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
333	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
334	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
335	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
336	C₄²×C₆₇	C₂⁴	1	4	yes	—
337	C₄²×C₆₇	C₂⁴	1	4	yes	—
338	C₄²×C₆₇	C₂⁴	1	4	yes	—
339	C₄²×C₆₇	C₂⁴	1	4	yes	—
340	C₄²×C₆₇	C₂⁴	1	16	yes	—
341	C₄²×C₆₇	C₂⁴	1	16	yes	—
342	C₄²×C₆₇	C₂⁴	1	8	yes	—
343	C₂³×C₆₇	—	2	4	no	—
344	C₂³×C₆₇	—	2	2	no	—
345	C₂³×C₆₇	—	2	4	no	—
346	C₂³×C₆₇	—	2	4	no	—
347	C₂³×C₆₇	—	2	2	no	—
348	C₂³×C₆₇	—	2	4	no	—
349	C₂³×C₆₇	—	2	4	no	—
350	C₂³×C₆₇	—	2	4	no	—
351	C₂³×C₆₇	—	2	4	no	—
352	C₂³×C₆₇	—	2	2	no	—
353	C₂³×C₆₇	—	2	4	no	—
354	C₂³×C₆₇	—	2	4	no	—
355	C₂³×C₆₇	C₂⁵	1	4	yes	—
356	C₂³×C₆₇	C₂⁵	1	2	yes	—
357	C₂³×C₆₇	C₂⁵	1	4	yes	—
358	C₂³×C₆₇	C₂⁵	1	4	yes	—
359	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
360	Q₈×C₆₇	—	2	8	no	—
361	Q₈×C₆₇	—	2	16	no	—
362	Q₈×C₆₇	—	4	16	no	—
363	Q₈×C₆₇	—	4	8	no	—
364	Q₈×C₆₇	—	4	8	no	—
365	D₄×C₆₇	—	2	8	no	—
366	D₄×C₆₇	—	2	8	no	—
367	D₄×C₆₇	—	2	8	no	—
368	D₄×C₆₇	—	4	8	no	—
369	D₄×C₆₇	—	4	8	no	—
370	D₄×C₆₇	—	4	16	no	—
371	D₄×C₆₇	—	4	8	no	—
372	D₄×C₆₇	—	4	8	no	—
373	D₄×C₆₇	—	4	8	no	—
374	D₄×C₆₇	—	4	16	no	—
375	C₂×C₄×C₆₇	—	2	4	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	4	no	—
378	C₂×C₄×C₆₇	—	2	8	no	—
379	C₂×C₄×C₆₇	—	2	4	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	4	no	—
382	C₂×C₄×C₆₇	—	2	4	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	8	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	16	no	—
387	C₂×C₄×C₆₇	—	2	16	no	—
388	C₂×C₄×C₆₇	—	2	8	no	—
389	C₂×C₄×C₆₇	—	2	8	no	—
390	C₂×C₄×C₆₇	—	2	16	no	—
391	C₂×C₄×C₆₇	—	4	16	no	—
392	C₂×C₄×C₆₇	—	4	4	no	—
393	C₂×C₄×C₆₇	—	4	16	no	—
394	C₂×C₄×C₆₇	—	4	16	no	—
395	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
396	C₂×C₄×C₆₇	2₋¹⁺⁴	1	4	yes	—
397	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
398	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
399	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
400	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
401	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
402	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
403	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
404	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
405	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
406	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
407	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
408	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
409	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
410	C₂²×C₆₇	—	2	4	no	—
411	C₂²×C₆₇	—	2	2	no	—
412	C₂²×C₆₇	—	2	4	no	—
413	C₂²×C₆₇	—	2	4	no	—
414	C₂²×C₆₇	—	2	2	no	—
415	C₂²×C₆₇	—	2	4	no	—
416	C₂²×C₆₇	—	2	4	no	—
417	C₂²×C₆₇	—	2	4	no	—
418	C₂²×C₆₇	—	2	4	no	—
419	C₂²×C₆₇	—	2	2	no	—
420	C₂²×C₆₇	—	2	4	no	—
421	C₂²×C₆₇	—	2	4	no	—
422	C₂²×C₆₇	—	4	8	no	—
423	C₂²×C₆₇	—	4	4	no	—
424	C₂²×C₆₇	—	4	8	no	—
425	C₂²×C₆₇	—	4	8	no	—
426	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
427	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
428	C₂²×C₆₇	#585	1	2	yes	—
429	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
430	C₄×C₆₇	—	2	4	no	—
431	C₄×C₆₇	—	2	2	no	—
432	C₄×C₆₇	—	2	4	no	—
433	C₄×C₆₇	—	2	8	no	—
434	C₄×C₆₇	—	2	4	no	—
435	C₄×C₆₇	—	2	2	no	—
436	C₄×C₆₇	—	2	4	no	—
437	C₄×C₆₇	—	2	4	no	—
438	C₄×C₆₇	—	2	2	no	—
439	C₄×C₆₇	—	2	8	no	—
440	C₄×C₆₇	—	2	2	no	—
441	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
442	C₄×C₆₇	C₂×2₋¹⁺⁴	1	4	yes	—
443	C₂×#3547	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂×C₆₇	—	4	4	no	—
445	C₂×C₆₇	—	4	2	no	—
446	C₂×C₆₇	—	4	4	no	—
447	C₂×C₆₇	—	4	4	no	—
448	C₂×C₆₇	#3547	1	4	yes	direct product factor
449	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂×C₆₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
451	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
452	#3547	C₂×C₆₇	1	32	yes	direct product factor
453	C₂×#562	C₂×C₆₇	1	4	yes	complemented
454	C₂×#555	C₂×C₆₇	1	2	yes	complemented
455	C₂×#555	C₂×C₆₇	1	1	yes	characteristic, complemented
456	C₂×#554	C₂×C₆₇	1	1	yes	characteristic, complemented
457	C₂×#553	C₂×C₆₇	1	2	yes	complemented
458	C₂×#552	C₂×C₆₇	1	2	yes	complemented
459	C₂×D₄×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
460	C₂×#548	C₂×C₆₇	1	2	yes	complemented
461	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
462	C₂×#544	C₂×C₆₇	1	2	yes	complemented
463	C₂×#542	C₂×C₆₇	1	4	yes	complemented
464	C₂×#540	C₂×C₆₇	1	2	yes	complemented
465	C₂×#537	C₂×C₆₇	1	2	yes	complemented
466	C₂×#536	C₂×C₆₇	1	2	yes	complemented
467	C₂×#533	C₂×C₆₇	1	1	yes	characteristic, complemented
468	C₂×#532	C₂×C₆₇	1	1	yes	characteristic, complemented
469	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
470	C₆₇	C₂×#3547	1	1	yes	characteristic, direct product factor, Sylow
471	C₂²×#41	C₂²×C₆₇	1	2	yes	—
472	C₂²×#41	C₂²×C₆₇	1	2	yes	—
473	C₂³×Q₈	C₂²×C₆₇	1	2	yes	—
474	#562	C₂²×C₆₇	1	64	yes	complemented
475	#555	C₂²×C₆₇	1	32	yes	complemented
476	#555	C₂²×C₆₇	1	16	yes	complemented
477	#554	C₂²×C₆₇	1	16	yes	complemented
478	#553	C₂²×C₆₇	1	32	yes	complemented
479	#552	C₂²×C₆₇	1	32	yes	complemented
480	D₄×Q₈	C₂²×C₆₇	1	16	yes	complemented
481	#548	C₂²×C₆₇	1	32	yes	complemented
482	#547	C₂²×C₆₇	1	16	yes	complemented
483	#544	C₂²×C₆₇	1	32	yes	complemented
484	#542	C₂²×C₆₇	1	64	yes	complemented
485	#540	C₂²×C₆₇	1	32	yes	complemented
486	#537	C₂²×C₆₇	1	32	yes	complemented
487	#536	C₂²×C₆₇	1	32	yes	complemented
488	#533	C₂²×C₆₇	1	16	yes	complemented
489	#532	C₂²×C₆₇	1	16	yes	complemented
490	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
491	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
492	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×C₄⋊Q₈	C₂²×C₆₇	1	4	yes	—
494	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
495	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
496	#529	C₂²×C₆₇	1	16	yes	complemented
497	C₂×#126	C₂²×C₆₇	1	2	yes	—
498	C₂×#126	C₂²×C₆₇	1	4	yes	—
499	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
500	C₂×#125	C₂²×C₆₇	1	2	yes	—
501	C₂×#125	C₂²×C₆₇	1	4	yes	—
502	C₂×#125	C₂²×C₆₇	1	2	yes	—
503	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
504	C₂×#124	C₂²×C₆₇	1	2	yes	—
505	C₂×#124	C₂²×C₆₇	1	4	yes	—
506	C₂×#124	C₂²×C₆₇	1	4	yes	—
507	C₂×#124	C₂²×C₆₇	1	4	yes	—
508	C₂×#123	C₂²×C₆₇	1	2	yes	—
509	C₂×#123	C₂²×C₆₇	1	4	yes	—
510	C₂×#123	C₂²×C₆₇	1	4	yes	—
511	C₂×#123	C₂²×C₆₇	1	4	yes	—
512	C₂×#123	C₂²×C₆₇	1	4	yes	—
513	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
514	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
515	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
516	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
517	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
518	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
519	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
520	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
521	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
522	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
523	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
524	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
525	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
526	C₂×#121	C₂²×C₆₇	1	2	yes	—
527	C₂×#121	C₂²×C₆₇	1	4	yes	—
528	C₂×#121	C₂²×C₆₇	1	2	yes	—
529	C₂×#121	C₂²×C₆₇	1	4	yes	—
530	C₂×#121	C₂²×C₆₇	1	4	yes	—
531	C₂×#121	C₂²×C₆₇	1	2	yes	—
532	C₂×#121	C₂²×C₆₇	1	4	yes	—
533	C₂×#121	C₂²×C₆₇	1	2	yes	—
534	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
535	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
536	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
537	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
538	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
539	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
540	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
541	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
542	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
543	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
544	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
545	C₂×#117	C₂²×C₆₇	1	2	yes	—
546	C₂×#117	C₂²×C₆₇	1	2	yes	—
547	C₂×#117	C₂²×C₆₇	1	2	yes	—
548	C₂×#117	C₂²×C₆₇	1	4	yes	—
549	C₂×#117	C₂²×C₆₇	1	2	yes	—
550	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
551	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
552	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
553	C₂×#41	—	4	8	no	—
554	C₂×#41	—	4	8	no	—
555	C₂×#41	C₂³×C₆₇	1	16	yes	—
556	C₂×#41	C₂³×C₆₇	1	16	yes	—
557	C₂²×Q₈	—	4	8	no	—
558	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
559	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
560	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
561	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
562	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
563	C₂²×Q₈	C₂³×C₆₇	1	16	yes	—
564	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
565	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
568	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
569	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
570	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
571	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
572	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
573	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
574	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
575	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
576	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
578	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
580	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
581	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
582	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
583	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
584	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
585	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
586	C₄⋊Q₈	C₂³×C₆₇	1	32	yes	—
587	C₄⋊Q₈	C₂³×C₆₇	1	16	yes	—
588	#127	C₂³×C₆₇	1	8	yes	—
589	#126	C₂³×C₆₇	1	16	yes	—
590	#126	C₂³×C₆₇	1	32	yes	—
591	#125	C₂³×C₆₇	1	8	yes	—
592	#125	C₂³×C₆₇	1	16	yes	—
593	#125	C₂³×C₆₇	1	32	yes	—
594	#125	C₂³×C₆₇	1	16	yes	—
595	#124	C₂³×C₆₇	1	8	yes	—
596	#124	C₂³×C₆₇	1	16	yes	—
597	#124	C₂³×C₆₇	1	32	yes	—
598	#124	C₂³×C₆₇	1	32	yes	—
599	#124	C₂³×C₆₇	1	32	yes	—
600	#123	C₂³×C₆₇	1	16	yes	—
601	#123	C₂³×C₆₇	1	32	yes	—
602	#123	C₂³×C₆₇	1	32	yes	—
603	#123	C₂³×C₆₇	1	32	yes	—
604	#123	C₂³×C₆₇	1	32	yes	—
605	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
606	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
607	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
608	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
609	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
610	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
611	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
612	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
613	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
614	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
615	#121	C₂³×C₆₇	1	8	yes	—
616	#121	C₂³×C₆₇	1	8	yes	—
617	#121	C₂³×C₆₇	1	8	yes	—
618	#121	C₂³×C₆₇	1	16	yes	—
619	#121	C₂³×C₆₇	1	32	yes	—
620	#121	C₂³×C₆₇	1	16	yes	—
621	#121	C₂³×C₆₇	1	32	yes	—
622	#121	C₂³×C₆₇	1	32	yes	—
623	#121	C₂³×C₆₇	1	16	yes	—
624	#121	C₂³×C₆₇	1	32	yes	—
625	#121	C₂³×C₆₇	1	16	yes	—
626	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
627	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
628	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
629	C₄×D₄	C₂³×C₆₇	1	8	yes	—
630	C₄×D₄	C₂³×C₆₇	1	16	yes	—
631	C₄×D₄	C₂³×C₆₇	1	8	yes	—
632	C₄×D₄	C₂³×C₆₇	1	16	yes	—
633	C₄×D₄	C₂³×C₆₇	1	8	yes	—
634	C₄×D₄	C₂³×C₆₇	1	16	yes	—
635	C₄×D₄	C₂³×C₆₇	1	16	yes	—
636	C₄×D₄	C₂³×C₆₇	1	32	yes	—
637	#117	C₂³×C₆₇	1	16	yes	—
638	#117	C₂³×C₆₇	1	16	yes	—
639	#117	C₂³×C₆₇	1	16	yes	—
640	#117	C₂³×C₆₇	1	32	yes	—
641	#117	C₂³×C₆₇	1	16	yes	—
642	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
647	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
648	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	—
649	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	—
650	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
655	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
659	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
660	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
661	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
678	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
679	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
680	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
682	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
686	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
687	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
688	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
689	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
690	#41	—	4	32	no	—
691	#41	—	4	32	no	—
692	C₂×Q₈	—	2	4	no	—
693	C₂×Q₈	—	2	8	no	—
694	C₂×Q₈	—	4	8	no	—
695	C₂×Q₈	—	4	4	no	—
696	C₂×Q₈	—	4	4	no	—
697	C₂×Q₈	—	4	32	no	—
698	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
699	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
700	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
701	C₂×Q₈	C₂⁴×C₆₇	1	16	yes	—
702	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	4	4	no	—
709	C₂×D₄	—	4	8	no	—
710	C₂×D₄	—	4	4	no	—
711	C₂×D₄	—	4	4	no	—
712	C₂×D₄	—	4	8	no	—
713	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
714	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
715	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
716	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
717	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
718	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
719	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
720	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
721	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
722	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
723	C₂²×C₄	—	2	8	no	—
724	C₂²×C₄	—	2	8	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	8	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	4	8	no	—
729	C₂²×C₄	—	4	8	no	—
730	C₂²×C₄	—	4	8	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
736	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
740	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
741	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
744	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
746	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
747	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
748	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
749	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
750	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
751	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
752	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
754	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
755	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
756	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
757	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
758	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
759	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
760	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
761	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
762	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
763	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
764	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
765	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
766	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
767	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
768	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
769	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
770	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
771	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
772	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
773	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
774	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
775	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
776	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
777	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
778	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
779	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
780	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
781	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
782	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
783	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
784	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
785	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
786	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
787	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
788	C₄²	C₂⁴×C₆₇	1	4	yes	—
789	C₄²	C₂⁴×C₆₇	1	4	yes	—
790	C₄²	C₂⁴×C₆₇	1	4	yes	—
791	C₄²	C₂⁴×C₆₇	1	4	yes	—
792	C₄²	C₂⁴×C₆₇	1	16	yes	—
793	C₄²	C₂⁴×C₆₇	1	16	yes	—
794	C₄²	C₂⁴×C₆₇	1	8	yes	—
795	C₂³	—	2	4	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	4	no	—
798	C₂³	—	2	4	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	4	no	—
801	C₂³	—	2	4	no	—
802	C₂³	—	2	4	no	—
803	C₂³	—	2	4	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	4	no	—
806	C₂³	—	2	4	no	—
807	C₂³	C₂⁵×C₆₇	1	4	yes	—
808	C₂³	C₂⁵×C₆₇	1	2	yes	—
809	C₂³	C₂⁵×C₆₇	1	4	yes	—
810	C₂³	C₂⁵×C₆₇	1	4	yes	—
811	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
812	Q₈	—	2	8	no	—
813	Q₈	—	2	16	no	—
814	Q₈	—	4	16	no	—
815	Q₈	—	4	8	no	—
816	Q₈	—	4	8	no	—
817	D₄	—	2	8	no	—
818	D₄	—	2	8	no	—
819	D₄	—	2	8	no	—
820	D₄	—	4	8	no	—
821	D₄	—	4	8	no	—
822	D₄	—	4	8	no	—
823	D₄	—	4	16	no	—
824	D₄	—	4	8	no	—
825	D₄	—	4	8	no	—
826	D₄	—	4	16	no	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	2	8	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	4	no	—
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	8	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	16	no	—
839	C₂×C₄	—	2	16	no	—
840	C₂×C₄	—	2	8	no	—
841	C₂×C₄	—	2	8	no	—
842	C₂×C₄	—	2	16	no	—
843	C₂×C₄	—	4	16	no	—
844	C₂×C₄	—	4	16	no	—
845	C₂×C₄	—	4	16	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
848	C₂×C₄	2₋¹⁺⁴×C₆₇	1	4	yes	—
849	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
850	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
851	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
852	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
853	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
854	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
855	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
856	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
857	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
858	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
859	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
860	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
861	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
862	C₂²	—	2	4	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	4	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	4	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	4	8	no	—
875	C₂²	—	4	4	no	—
876	C₂²	—	4	8	no	—
877	C₂²	—	4	8	no	—
878	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
879	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
880	C₂²	#585×C₆₇	1	2	yes	—
881	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
882	C₄	—	2	4	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	4	no	—
885	C₄	—	2	8	no	—
886	C₄	—	2	4	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	4	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	8	no	—
892	C₄	—	2	2	no	—
893	C₄	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
894	C₄	C₂×2₋¹⁺⁴×C₆₇	1	4	yes	—
895	C₂	—	4	4	no	—
896	C₂	—	4	2	no	—
897	C₂	—	4	4	no	—
898	C₂	—	4	4	no	—
899	C₂	C₆₇×#3547	1	4	yes	direct product factor
900	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
901	C₂	C₂²×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
902	C₂	C₂×#585×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₆₇×#3547	C₂	direct (N × H)
2. C₂×#562×C₆₇	C₂	semidirect
3. C₂×#555×C₆₇	C₂	semidirect
4. C₂×#555×C₆₇	C₂	semidirect
5. C₂×#554×C₆₇	C₂	semidirect
6. C₂×#553×C₆₇	C₂	semidirect
7. C₂×#552×C₆₇	C₂	semidirect
8. C₂×D₄×Q₈×C₆₇	C₂	semidirect
9. C₂×#548×C₆₇	C₂	semidirect
10. C₂×#547×C₆₇	C₂	semidirect
11. C₂×#544×C₆₇	C₂	semidirect
12. C₂×#542×C₆₇	C₂	semidirect
13. C₂×#540×C₆₇	C₂	semidirect
14. C₂×#537×C₆₇	C₂	semidirect
15. C₂×#536×C₆₇	C₂	semidirect
16. C₂×#533×C₆₇	C₂	semidirect
17. C₂×#532×C₆₇	C₂	semidirect
18. C₂×#529×C₆₇	C₂	semidirect
22. #562×C₆₇	C₂²	semidirect
23. #555×C₆₇	C₂²	semidirect
24. #555×C₆₇	C₂²	semidirect
25. #554×C₆₇	C₂²	semidirect
26. #553×C₆₇	C₂²	semidirect
27. #552×C₆₇	C₂²	semidirect
28. D₄×Q₈×C₆₇	C₂²	semidirect
29. #548×C₆₇	C₂²	semidirect
30. #547×C₆₇	C₂²	semidirect
31. #544×C₆₇	C₂²	semidirect
32. #542×C₆₇	C₂²	semidirect
33. #540×C₆₇	C₂²	semidirect
34. #537×C₆₇	C₂²	semidirect
35. #536×C₆₇	C₂²	semidirect
36. #533×C₆₇	C₂²	semidirect
37. #532×C₆₇	C₂²	semidirect
44. #529×C₆₇	C₂²	semidirect
443. C₂×#3547	C₆₇	direct (N × H)
448. C₂×C₆₇	#3547	direct (N × H)
452. #3547	C₂×C₆₇	direct (N × H)
453. C₂×#562	C₂×C₆₇	semidirect
454. C₂×#555	C₂×C₆₇	semidirect
455. C₂×#555	C₂×C₆₇	semidirect
456. C₂×#554	C₂×C₆₇	semidirect
457. C₂×#553	C₂×C₆₇	semidirect
458. C₂×#552	C₂×C₆₇	semidirect
459. C₂×D₄×Q₈	C₂×C₆₇	semidirect
460. C₂×#548	C₂×C₆₇	semidirect
461. C₂×#547	C₂×C₆₇	semidirect
462. C₂×#544	C₂×C₆₇	semidirect
463. C₂×#542	C₂×C₆₇	semidirect
464. C₂×#540	C₂×C₆₇	semidirect
465. C₂×#537	C₂×C₆₇	semidirect
466. C₂×#536	C₂×C₆₇	semidirect
467. C₂×#533	C₂×C₆₇	semidirect
468. C₂×#532	C₂×C₆₇	semidirect
469. C₂×#529	C₂×C₆₇	semidirect
470. C₆₇	C₂×#3547	direct (N × H)
474. #562	C₂²×C₆₇	semidirect
475. #555	C₂²×C₆₇	semidirect
476. #555	C₂²×C₆₇	semidirect
477. #554	C₂²×C₆₇	semidirect
478. #553	C₂²×C₆₇	semidirect
479. #552	C₂²×C₆₇	semidirect
480. D₄×Q₈	C₂²×C₆₇	semidirect
481. #548	C₂²×C₆₇	semidirect
482. #547	C₂²×C₆₇	semidirect
483. #544	C₂²×C₆₇	semidirect
484. #542	C₂²×C₆₇	semidirect
485. #540	C₂²×C₆₇	semidirect
486. #537	C₂²×C₆₇	semidirect
487. #536	C₂²×C₆₇	semidirect
488. #533	C₂²×C₆₇	semidirect
489. #532	C₂²×C₆₇	semidirect
496. #529	C₂²×C₆₇	semidirect
899. C₂	C₆₇×#3547	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₇×#3547	2
C₂×#562×C₆₇	2
C₂×#555×C₆₇	2
C₂×#554×C₆₇	2
C₂×#553×C₆₇	2
C₂×#552×C₆₇	2
C₂×D₄×Q₈×C₆₇	2
C₂×#548×C₆₇	2
C₂×#547×C₆₇	2
C₂×#544×C₆₇	2
C₂×#542×C₆₇	2
C₂×#540×C₆₇	2
C₂×#537×C₆₇	2
C₂×#536×C₆₇	2
C₂×#533×C₆₇	2
C₂×#532×C₆₇	2
C₂×#529×C₆₇	2
C₂×#3547	67

Subgroups — C2×C67×#3547 #30742001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3547 #30742001